Some Critical Properties of the Eight-Vertex Model

Abstract

The eight-vertex model solved by Baxter is shown to be equivalent to two Ising models with nearest-neighbor coupling interacting with one another via a four-spin coupling term. The critical properties of the model in the weak-coupling limit are in agreement with the scaling hypothesis. In this limit where $\alpha \to 0$, the critical indices obey $\frac{\gamma }{{\gamma }_0}=\frac{\beta }{{\beta }_0}=\frac{\nu }{{\nu }_0}=1-\frac{1}{2}\alpha$, $\frac{\delta }{{\delta }_0}=\frac{\eta }{{\eta }_0}=1\mathrm{}$, with the subscripts zero denoting the index values for the ordinary two-dimensional Ising model.